What happens if someone driving my car wrecked it without permission?

Definitely call her insurance and make a claim first. Only if she has no insurance will you have to check into your own collision insurance.

The reason you have insurance is to protect you in the event that your car, or anyone driving it with your permission, is responsible for causing an accident and resulting injury. While the driver's insurance should be primary on the injury claims, if there are any, your insurance should be primary on your property damage claim. While her insurance may be willing to pay for your property damage, the reason you have insurance is to repair your vehicle when it is damaged, whether your fault or not. You have a first party contractual relationship with your carrier and as a result they must treat you fairly, while you have no such relationship with the driver's insurance. Therefore, they don't have to repair disputed damage, nor do they have to repair it in a reasonable period of time. If you pursue repairs through your own carrier, they will subrogate the amount they pay to repair your vehicle, meaning they will pursue reimbursement from the driver's carrier. Therefore, instead of dealing with a company with which you have no relationship and hence no real leverage over, you should pursue your property damage repairs through your own carrier and let them go get it from the other company. Given the accident is not your fault and your carrier will be getting reimbursement there should be no adverse effect on your premiums.

At a minimum, you should file a claim against her own insurance policy. You may also need to file a police report to prove that she did not have permission to take the car.